Variation in reproductive success

$$N_e = \frac{2N}{1+\frac{\sigma^2}{\bar k}} \quad,$$

where $\sigma^2$ is the variance in family size among individuals and $\bar k$ is the average number of offspring per individual.

If $\sigma^2 = 0$, $N_e = 2N$. If $\sigma^2 = 3\bar k$, $N_e = N/2$. Suppose, for example that the distribution of offspring number is negative binomial with mean 2 and variance 12.⁵ Then $N_e = \frac{2N}{1+(12/2)} \approx 0.28N$.

Management implication - Reducing the differences among individuals in the number of offspring they produce can almost halve the susceptibility of a population to random genetic changes. There is a complication worth noting here, however. What I just said is true with respect to loss of genetic diversity as a result of genetic drift, but it's true only if the population size is constant with respect to the increase in relatedness among individuals in the population.⁶ If the population size is increasing the effective size is close to size of progeny population (not parental population) and equal reproduction increases the effective population size by less than a factor of two. In fact, if the population size is increasing rapidly enough, equalizing the reproductive success of parents would cause relatedness to accumulate more rapidly if it limits the rate of population growth.